A Comprehensive Introduction to Differential Geometry

Michael Spivak's A Comprehensive Introduction to Differential Geometry, 3rd Edition, is the classic five-volume treatment of the subject, from manifolds and differential forms through the Gauss-Bonnet-Chern theorem. Every volume is available individually or as a complete set, printed and bound by the original publisher, Publish or Perish, Inc. Each volume's page links to its complete table of contents.

Volumes 1 and 2 are also the prerequisite Spivak names for his Physics for Mathematicians, Mechanics I, which carries the same language into classical mechanics.